Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+2y &= -8 \\ -6x+y &= -3\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {6x-3}$ Substitute this expression for $y$ in the first equation. $4x+2({6x - 3}) = -8$ $4x + 12x - 6 = -8$ Simplify by combining terms, then solve for $x$ $16x - 6 = -8$ $16x = -2$ $x = -\dfrac{1}{8}$ Substitute $-\dfrac{1}{8}$ for $x$ back into the top equation. $4( -\dfrac{1}{8})+2y = -8$ $-\dfrac{1}{2}+2y = -8$ $2y = -\dfrac{15}{2}$ $y = -\dfrac{15}{4}$ The solution is $\enspace x = -\dfrac{1}{8}, \enspace y = -\dfrac{15}{4}$.